Benhamou Simon
Behavioral Ecology Group, Centre d'Ecologie Fonctionnelle et Evolutive, Centre National de la Recherche Scientifique, Montpellier, France.
Ecology. 2007 Aug;88(8):1962-9. doi: 10.1890/06-1769.1.
Lévy walks (LW) are superdiffusive and scale-free random walks that have recently emerged as a new conceptual tool for modeling animal search paths. They have been claimed to be more efficient than the "classical" random walks, and they also seem able to account for the actual search patterns of various species. This suggests that many animals may move using a LW process. LW patterns look like the actual search patterns displayed by animals foraging in a patchy environment, where extensive and intensive searching modes alternate, and which can be generated by a mixture of classical random walks. In this context, even elementary composite Brownian walks are more efficient than LW but may be confounded with them because they present apparent move-length-heavy tail distributions and superdiffusivity. The move-length "survival" distribution (i.e., the cumulative number of moves greater than any given threshold) appears to be a better means to highlight a LW pattern. Even once such a pattern has been clearly identified, it remains to determine how it was actually generated, because a LW pattern is not necessarily produced by a LW process but may emerge from the way the animal interacted with the environment structure through more classical movement processes. In any case, emergent movement patterns should not be confused with the processes that gave rise to them.
列维游走（LW）是超扩散且无标度的随机游走，最近已成为一种用于模拟动物搜索路径的新概念工具。据称它们比“经典”随机游走更高效，而且似乎还能解释各种物种的实际搜索模式。这表明许多动物可能通过列维游走过程移动。列维游走模式类似于动物在斑块状环境中觅食时所展示的实际搜索模式，在这种环境中广泛搜索和密集搜索模式交替出现，并且可以由经典随机游走的混合产生。在这种情况下，即使是基本的复合布朗游走也比列维游走更高效，但可能会与它们混淆，因为它们呈现出明显的步长重尾分布和超扩散性。步长“存活”分布（即大于任何给定阈值的移动累积数量）似乎是突出列维游走模式的更好方法。即使这样的模式已被明确识别，仍需确定它实际上是如何产生的，因为列维游走模式不一定由列维游走过程产生，而是可能通过动物与环境结构通过更经典的运动过程相互作用的方式出现。无论如何，涌现的运动模式不应与产生它们的过程相混淆。
